I am not sure that I understand you — how is the capacity of the mind to perceive reality related to the particle/math comparison?
Feynman sought to predict particle interactions, by adding together all the possible interaction paths. That sum is what we observe, so that sum is analogous to the sum of maths. Yet, that analogy does not make them interchangeable. The maths being combined are each a different set of axioms. One math = multiple axioms as its foundation; another math = different axioms as foundation. A particle is not a set of axioms. Though, if you sum all these axiomatic systems’ behaviors, analogous to the sum of particle paths, then the only remaining axiomatic sets are those which allow intelligent systems.